With traditional life insurance (NOT accidental death and dismemberment insurance), the policy will cover dying of old age. Of course, the life insurance policy must be in effect at the time of death, which necessitates that it does not lapse or become cost prohibitive before reaching one's advanced years.
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Once a fully underwritten life insurance policy is past the contestability period with no policy exemptions, it will pay proceeds on the death of the insured, cause of death notwithstanding. Old age is somewhat esoteric in these days of living to age 100, but "dying of old age" may be defined as any age at death past actuarial life expectancy.
Here are some tips on obtaining coverage that will pay in old age. http://ezinearticles.com/?Final-Expense-Funeral-Insurance&id=2418597